Volume 7, Issue 3
1999

An efficient algorithm is presented to "zonohedrify" a given polyhedron. There are relatively few interesting processes which input an arbitrary polyhedron and output a related polyhedron.  Well-known examples are truncation, stellation, dualization (reciprocation in a sphere), and compounding.  To this list can be added zonohedrification, in which the vertex directions of the original polyhedron (relative to an arbitrary center) determine the edge directions of the resulting zonohedrification.  A few mathematical properties of zonohedra are outlined to give the reader insight into zonohedral structure and an understanding of the algorithm. 

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Additional Materials

• zonohedra1.nb (generates all examples)
• Towle.nb (enhanced version by Russell Towle)

(If you don't have a copy of Mathematica, you can view the notebook using Mathematica Player.)

George W. Hart is the author of Multidimensional Analysis, the web site The Encyclopedia of Polyhedra  (www.georgehart.com), and the upcoming Zome Geometry (Key Curriculum Press). Some of his sculptural works are exhibited at the University of California at Berkeley, Princeton University, and the Long Island Museum of Science and Technology. He holds a B.S. in Mathematics and a Ph.D. in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology.